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Abelian categories, almost split sequences, and comodules
Authors:Mark Kleiner   Idun Reiten
Affiliation:Department of Mathematics, Syracuse University, Syracuse, New York 13244-1150 ; Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491 Trondheim, Norway
Abstract:The following are equivalent for a skeletally small abelian Hom-finite category over a field with enough injectives and each simple object being an epimorphic image of a projective object of finite length.

(a) Each indecomposable injective has a simple subobject.

(b) The category is equivalent to the category of socle-finitely copresented right comodules over a right semiperfect and right cocoherent coalgebra such that each simple right comodule is socle-finitely copresented.

(c) The category has left almost split sequences.

Keywords:Abelian category   almost split sequence   semiperfect cocoherent coalgebra   comodule
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